Design of current digital electronics systems use sophisticated modeling techniques to analyze every aspect of device behavior. While functional performance and parametric specifications such as propagation delay and clock speed receive a large share of attention in a device analysis, increasing effort is being devoted to system environment concerns including noise environment behavior.
In a digital device, signals are routed using metallic interconnect of very small dimensions often separated by only minute distances from possible sources of signal interference. Advancing technologies have caused interconnect dimensions and spacing to undergo reductions. These effects dictate that increasing attention be given to analysis of noise and cross-talk performance. The challenge of such analysis has been heightened as it has been noted that noise and cross-talk are often highly non-linear in character.
Typically, conventional forms of analysis avoid the use of complex metrics and employ simplified models leading to analysis that has lacked accuracy. It has become increasingly clear that improved methods of noise analysis are necessary. Although designers have long been aware of the types of noise that must be dealt with, seldom have the analytical tools been available to adequately assess the problem and provide effective solutions. Cross-talk effects are of increasing interest because the problem of cross-talk has been pervasive and the tools to analyze it have been inadequate.
Conventional cross-talk noise analysis is based on consideration of the interaction of multiple victim gates with an aggressor cross-talk noise source illustrated in FIG. 1. The output of primary victim gate 101 is connected to the input of a secondary victim gate 102. Cross-talk noise analysis is intended to evaluate the sensitivity of gate 101 to aggressor cross-talk noise-at node 105 coupled to output node 111 via parasitic capacitance 109 and the effect this cross-talk noise at node 105 has in producing a false logic at input node 111 of secondary victim gate 102 that exceeds the noise immunity of gate 102. The primary victim gate 101 is viewed as a structure that generates an output current Iout1(t) 107 as a function of an input voltage Vin 1(t) 110. Gate 100 couples into the primary victim gate 101 at node 110 and output signal 112 is used to display and analyze possible false logic level disturbances that result from the cross-talk noise. The analysis typically keys on the effects that a non-ideal input condition at node 110 have exacerbating the aggressor cross-talk noise coupled into node 111. This non-ideal input condition can be a result of additional actual noise coupled to node 110 or insufficient drive strength of gate 100 driving node 110.
FIG. 2 illustrates the circuit of a typical CMOS inverter gate 200 composed of a PMOS transistor 201 and an NMOS transistor 202 connected in tandem between supply voltage VDD 203 and ground voltage VSS (GND) 204. Assuming static (DC) conditions, gate 200 input voltage is VIN 205 and gate 200 output voltage is VOUT 210. The drain current in full ‘on’ condition for the PMOS transistor 201 is denoted by IP 206 and the drain current in full ‘on’ condition for the NMOS transistor 202 is denoted by IN 207. IOUT 208 equals the difference between the current drives of the PMOS and the NMOS transistor. This difference is designed to be in balance IP=IN at an input voltage VIN=VTHRESHOLD, the gate input threshold.
FIG. 3 illustrates the DC transfer function of the CMOS inverter of FIG. 2. The transfer function has three separate regions: (input low, output high) 301, (transition region) 302, and (input high, output low) 303. In ordinary analysis the separation between the transition region 302 and the non-transition regions 301, and 303 is marked by a slope=−1 (305, 306) in the transfer function curve. Operation in regions 301 and 303 is characterized by stable gate performance protected by noise immunity as noted by 307 and 308. Concise unequivocal definitions of noise immunity have always been the aim in developing noise-analysis techniques. We will assume that the lesser value of noise immunity NI 307 or NI 308 is to be used in noise immunity assumptions. We assign the label NI* to this lesser value.
FIG. 4 illustrates the conventional model of victim gates subjected to cross-talk noise. For convenience in the massive amount of calculations required for the analysis, the CMOS gate of FIG. 2 is replaced by a simplified model (shown as gate 401 of FIG. 4). Aggressor noise 405 is viewed as coupling to victim node 411 via parasitic capacitance 406 to the equivalent ideal DC static output resistance R* 403 of the victim gate. The R* value for an individual victim gate in a very large netlist of gates is easily determined by parametric extraction and the particular value of R* will depend, for example, on the transistor sizes of the victim gate of interest. The effect not properly accounted for in this conventional model is that the primary victim gate may have a non-ideal input condition arising from incomplete recovery to its static value. The value of R 403 is then in reality non-ideal, higher that the R* value, and more susceptible to coupling of noise across capacitor 406. The non-ideal condition at the primary victim gate 400 could also result from the simultaneous presence of noise at both the input 410 and the output 411 of the primary victim gate 400.
Conventional cross-talk analysis also uses the value of NI* developed graphically in FIG. 3 for the noise immunity as the criteria for generation of false logic levels at the secondary victim gate 402. Conventional computer aided circuit analysis on cross-talk noise effects, therefore, proceeds on these two simplifying assumptions:
1. The primary victim gate may be represented by a simple resistor model using R* as the equivalent output resistance value.
2. The noise immunity of the secondary victim gate is the DC noise immunity NI* of the CMOS gate of FIG. 3.
These two assumptions unfortunately do not take into account the effect that these quantified parameters R* and NI* are decoupled from one another and this leads to overly optimistic conclusions regarding susceptibility to cross-talk noise.